Work has progressed in family-based statistical methods for studying genetic effects on qualitative and quantitative traits. We had previously developed methods for qualitative traits using genotypes for affected individuals and their parents, and if possible their grandparents. The loglinear approach we had proposed provides a likelihood ratio test and estimation of relative penetrances for variant alleles without requiring knowledge of the genetic model and is robust against bias due to population stratification. The method can incorporate parent-of-origin effects, and maternally-mediated genetic effects, and allows for the possibility that one or both parental genotypes, or even the genotype of the affected offspring, may be missing. For early-onset conditions, grandparental genotypes can provide markedly improved statistical power, and we showed that a design that genotypes the maternal but not the paternal grandparents is almost fully efficient compared to a full grandparental design. This has immediate application in studies of causes of birth defects or pregnancy complications. We have now extended our general approach to mapping genes related to a quantitative trait, and we showed that our method provides improved power and robustness over analytic alternatives in widespread use. We also have extended the method to allow for multiple offspring from the same nuclear family. For early onset disorders, or traits such as birth weight or childhood adiposity, the prenatal environment can be particularly important and maternally-mediated genetic effects expressed during gestation can influence the phenotype of the offspring. An extension of our method for quantitative trait analysis allows the identification of maternally-mediated genetic effects and also for variant imprinted genes, where the expression of a singly inherited copy may depend on parent of origin. We have also extended our methods to allow for gene-by-environment interaction. Family-based studies cannot directly assess effects of exposures, which is a serious limitation; traditional case-control studies have different limitations. For example, they are subject to bias due to selection of controls and they cannot directly assess maternally mediated effects or imprinting. We have developed a hybrid design that includes both nuclear families and unrelated population controls, and thereby offers the best of both approaches. This hybrid design is considerably more powerful than either traditional approach and also provides a test for bias due to population stratification, a problem that can invalidate a population-based case-control study of genetic effects. If this problem is detected in a given hybrid study, the investigator retains the ability to fall back to the case-parents component of the study, which will remain valid for testing genetic effects and gene-by-environment interaction. This design is being implemented in ongoing studies of the birth defects oral clefting and anencephaly. Work has also begun on methods based on genotyping of pooled DNA samples in epidemiologic studies, using case-parent designs for a qualitative trait.